Multi-asset investing: Wizard of Odds
In probability theory the Kelly criterion is a way to decide the optimal size of a series of bets. It was discovered by a physicist named Kelly who figured out the idea when he was working in telecommunications research at Bell Labs in the 1950s. Kelly figured out the formula which showed the optimal amount to stake given the odds and the chance of winning a bet. His insights are reflected in the way that we actually manage multi-asset portfolios today.
In one famous study 61 people were invited to take a test. They were each given $25 and asked to bet on a biased coin that would land on heads 60% of the time. Every time they guessed the correct answer they doubled their money. Remarkably, given that the game had an expected return of 20% for each play, 28% of the participants went bust, and the average pay out was just $91. 18 of the 61 participants bet everything on one toss, while an astonishing two-thirds gambled on tails at some stage during the experiment. Neither approach is in the least bit optimal.
The Kelly strategy would work as follows. Based on the odds and chance of winning above, the optimal strategy is to bet 20%* of your pot on heads on each throw. So if you lose, you cut the size of your bet; if you win, your stake increases. Similarly if the odds of landing on heads dropped from 60% to 55% (assuming the coin in the experiment is now less biased), the optimal strategy is to bet 10% of your pot on heads on each throw.
So can the Kelly criterion teach us any lessons in the world of absolute return investing? Certainly - and in the case of building multi-asset portfolios the above results are intuitive. The efficiency of an asset class is a measure of its expected return divided by its expected risk, so using Kelly logic above, more efficient asset classes would justify a larger proportion of portfolio holdings in a diversified asset mix. This is what portfolio construction and optimisation processes seek to achieve.
What is perhaps more interesting is the intuitive logic that the size of your portfolio holding should reflect the current view of expected return and expected risk. Optimal allocations change when prices change, because expected returns and expected risk change. Being dynamic in this area means you are pricing your positions with all of the most current available information.
Of course, in the real world, our multi-asset portfolio managers (PMs) face a much more complex scenario. The odds of success are seldom as clear-cut as in Kelly’s example, nor so static. The results of any decision are often not binary, instead in a complex world there can be a wide range of possible outcomes. Last but not least, the odds are not a given: our PMs need to compare their own assessment of probabilities to the market’s assessment in order to spot anomalies. Their goal is to identify asymmetry of risk and reward – where the market consensus has mispriced an asset such that it offers more upside than downside potential based on the available information. Frequently, our PMs use derivative strategies to exploit asymmetry in options pricing and to create upside potential whilst protecting their portfolios’ downside risk. The Kelly formula is a start point in real-world investing, but Kelly never progressed it to cope with all the complexities of dynamic multi-asset investing. If he had, who knows? He might have invented mobile phones too.
*The Kelly formula:
Edge / Odds = Fraction of capital that should be allocated
The edge is calculated by the total expected value, obtained by adding up the multiplication of each scenario’s possible outcome by its corresponding probability [0.6 x 1 - 0.4 x 1 = 0.2]
The odds are the positive outcome that can be obtained 
Crevan Begley, Client Strategy & Research, EMEA